Many clinically used articles need an aseptic packaging, for example, aseptic gloves, aseptic gauze, plaster, etc. The article 5.1.9c of the first part of Packaging for Terminally Sterilized medical instruments of ISO 11607-2006 which is applied at present prescribes that the peeling characteristics shall be continuous and homogenous, without delamination or tearing of the material that can affect aseptic opening and presentation. Article 7.3.5 of the Packaging for Terminally Sterilized Medical Instruments of GB/T 19633-2005 prescribes that in package-peeling, fiber falling and cracking or breaking off of the packaging material shall be in a specified limitation of a manufacturer to ensure no influence on the use of medical instruments. However, these standards, including pharmaceutical Industry Standards YY/T 0698, do not prescribe an inward curling degree of the peeling side of the packaging for the terminally sterilized medical instruments when peeled-open. At present, there are many types of medical aseptic packaging, for example, a pre-formed rigid tray is provided with a die-cut lid, flexible peel pouch, sterilization bag, header bag, form/fill/seal (FFS) and four-side-sealing (4SS) process, etc., (appendix A3 of the first part of ISO11607-2006), and one or both of the upper packaging surface and lower packaging surface of the packaging is usually soft. These aseptic packaging are provided with a peeling side/edge, i.e., an extending part (non-aseptic, a gripper part) outside the sealing edge that is wider than the other three sides. Of course, there are packaging with multiple peeling sides. In clinical practice, an operator peels the aseptic packaging, the operation standard requires that the peel-open flap is peeled while two faces (both soft) or one face (soft) of the packaging is turned outwardly and curled. In fact, when the peelable flap of the aseptic packaging is longer and cannot be grasped by the hands or the operator peels the package in a hasty manner, due to the influence of the non-peeled parts at two adjacent sides of the peelable flap, the part not grasped on the soft cover is turned inwardly and curled, and the germ-carrying extending part outside the sealing edge contacts with and contaminates contents, thereby increasing an infection risk. Further, damage from sealing fiber and scrap falling off of the packaging can lead to contamination of the contents. Therefore, there is a need for a controllable soft cover peeling direction of the packaging for aseptic medical instruments.